Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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3
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1answer
44 views

Is there a general term for $A\oplus B = \{a \oplus b | a\in A, b\in B\} $?

Is there a general term that specifies that if an operator $\oplus$ is applied to two sets, it's actually applied to all possible pairs of elements of the two sets? Or is that always the case and ...
1
vote
0answers
18 views

Correct term for higher-dimensional analogue of a cyclic polygon?

A $d$-dimensional polytope whose vertices lie on the boundary of some $d$-dimensional sphere is called a cyclic polygon when $d=2$. Is there a succinct name for this in higher dimensions?
1
vote
1answer
28 views

Explain Multidegree of a polynomial

Definition (The book Ideals, Varieties and Algorithms, Cox et al, pages 59-60 on 2008 edition): Let $f=\sum_a a_a x^a$ be a nonzero polynomial in $k[x_1,\ldots, x_n]$ and let > be a monomial ...
1
vote
0answers
28 views

Name for “3D quadrilateral” shape?

I am interested to know the name of the following solid construction - kind of a deformed cube... but I don't know the name, or even a general name: Left and right faces parallel with the $yz$ axes ...
2
votes
1answer
37 views

What is the precise relationship between vector space and vecctor field?

I have looked up precise definition of a vector field and a vector space but I could not understand the relationship between them. On wikipedia A vector field is: Given a subset $S$ in $R^n$, a ...
1
vote
0answers
9 views

Reference requests on SP -graphs to outline its research areas

I want to understand SP graphs (series-parallel graphs) deeper for more elegant computation. I want to understand which area to research to understand sp-graph deeper: logical formalism? ...
11
votes
2answers
120 views

What are the “numerator” and “denominator” of binomial coefficients called?

Do the numbers $n$ and $k$ in the binomial coefficient $\binom nk$ have a name? For the fraction $\frac nk$ we would use numerator and denominator. But I have not seen some terminology for binomial ...
2
votes
1answer
69 views

Less suggestive terms for “vector addition” and “scalar multiplication”

Question Are there less suggestive terms for the two operations commonly referred to as vector addition and scalar multiplication? Background In linear algebra, we use the terms vector addition and ...
12
votes
0answers
107 views

Name for a ring that also has composition - aka function application?

What is the following type of ring? Does it have a name? Suppose $(R,\cdot,+,0,1)$ is a ring with another binary operation, $\circ$ with the properties: $$(a\circ b)\circ c=a\circ(b\circ c)\\ ...
2
votes
0answers
16 views

Additive and Multiplicative Effects: Terminology

I am trying to explain the relationship between several variables. The outcome of interest is $Y \in \mathbb{R}$, and the predictors of interest are $A \in \mathbb{R}$ and $B \in \mathbb{R}_{>0}$. ...
2
votes
0answers
44 views

Matrix identification

Is there any name for a square, symmetric matrix, created in the following format: $$M_{i,j} = \left\{\begin{matrix} i + j & i \neq j\\ 0 & i = j \end{matrix}\right.$$ where $i, j$ start ...
1
vote
1answer
16 views

Identification of Independent and Dependent Variables

I often have trouble identifying what is the dependent variable and what is the independent variable in written English. Consider this: Dependence of A on B. In this case it's clear A is dependent ...
-1
votes
1answer
61 views

The name of the sum $\sum_{i=0}^n \frac{1}{m-i}$

Sorry for the vague question name, since I am looking for the name of the series. Also this might not be a "series" by the strict definition of a series.. anyways here it is: Choose some $m$ and $n$ ...
0
votes
0answers
13 views

Word for One-Radian Sector

Is there a technical term for the sector of a circle that corresponds to 1 radian? For example, assuming a pizza pie is a circle, is there a word to describe the slice that is exactly 1 radian (about ...
3
votes
1answer
43 views

Name of property: $g(f(a), f(b)) = f(g(a, b))$

What's the name of the property of the functions $f$ and $g$ that lets one do this: $g(f(a),f(b))=f(g(a,b))$ For example, I'm looking for a certain class of functions that do this: $f(a) \oplus ...
1
vote
2answers
26 views

What does “the subgroups of $G$ form a chain” mean?

I am being asked to show that: $G$ is a cyclic $p$-group $\iff$ its subgroups form a chain. What does "its subgroups form a chain" mean? Please keep in mind that I am just asking for the meaning of ...
3
votes
3answers
84 views

Is there a relationship between isometry as defined on metric spaces and those on vector spaces?

I am taking a course on linear algebra and another on real analysis. In linear algebra we defined that two vector spaces are isomorphic if there existed a bijective and linear map between ...
-1
votes
0answers
37 views

What is the name of the test that is used to test whether a sequence $f_{n}$ is uniformly convergent?

As I understand there are two tests where you test whether a function is uniformly convergent. 1) Where you use $\epsilon>0$ and find $N$ such that $|f_{n}-f|<\epsilon$, $\forall n>N$, what ...
1
vote
0answers
35 views

What does $\log^3$ stand for in this paper by K. Győry?

In this paper from 1980 K. Győry proved an upper bound for the absolute value of the solutions to a given Thue-Mahler equation, but I don't understand what he meant with $\log^3$. Namely, consider a ...
2
votes
1answer
26 views

A circulant matrix and its transpose

It is well-known that a circulant matrix $A$ of size $n \times n$ is isomorphic to a polynomial $$p(x) \bmod x^n - 1.$$ If we consider the transpose $A^T$, what is the corresponding polynomial ...
0
votes
1answer
46 views

What is the name of the below method??

what is the name of the rule that calculates limits such as limit $\dfrac{x^6-64}{x^4-16}$ when $x$ tends to $2$ so the answer is $6/4$ times $2^{6-4}$ no L'Hopital's Rule and the general formula of ...
0
votes
0answers
10 views

Is there a terminology to denote a topological vector space that admits an inner product?

Let $(V,\tau)$ be a topological vector space over $\mathbb{K}$. If there is a norm $||\cdot||$ on $V$ such that the metric topology induced by $||\cdot||$ is $\tau$, then we call $V$ is normable. ...
1
vote
1answer
16 views

Is it more accurate to use the term Geometric Growth or Exponential Growth?

On Wikipedia, the terms Exponential Growth and Geometric Growth are listed as synonymous, and defined as ...
0
votes
0answers
18 views

Is continuous the same as uncountable in “continuous-time stochastic process”?

Is the word "continuous'' as used in "continuous-time stochastic process" or "continuous-time Markov chain'' synonymous with uncountable? Or is there a difference? I'm wondering because I have seen ...
1
vote
3answers
104 views

Name of this property: if $x * x = y * y \implies x = y$

Algebraically speaking, what's the name of this property?: $x * x = y * y \implies x = y$ $*$ being a binary operation
0
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0answers
24 views

Monic polynomial terminology

If the constant term of a monic polynomial is one or negative one, is there a name for that special kind of monic polynomial?
3
votes
1answer
57 views

What is the general term for concepts like length, area and volume?

In geometry, we have concepts such as length (of a 1-dimensional line), area (of a 2-dimensional square) and volume (of a 3-dimensional cube). What is the general term for these concepts, such that ...
0
votes
1answer
43 views

What is the origin of the name Hermitian and Unitary matrix?

A matrix $H$ is Hermitian if $H ^\dagger = H$. A matrix $U$ is Unitary if $U^\dagger=U^{-1}$. My question is: Why do we name matrices of such properties Hermitian and Unitary? These names are ...
0
votes
1answer
60 views

Meaning of imaginary number [duplicate]

I'm a bit confused about the true meaning of imaginary number. It's my understanding that a complex number is a number of the form $a+ib$, where $a$ and $b$ are real numbers. A pure imaginary number ...
0
votes
0answers
17 views

English wording for “first level of asymptotic expansion”

In French, we say that $f$ est équivalente à $g$ denoted by $f \sim g$ for a limit point $x_0$ of a topology when $$\lim\limits_{x \to x_0} \frac{f(x)}{g(x)} = 1.$$ This is the first level of ...
3
votes
1answer
58 views

What do you call a cardinal $\kappa$ that is a limit of $\kappa$-many cardinals?

For instance, $\omega$ is the limit of $\omega$-many cardinals. But of course $\omega_1$ is not the limit of $\omega_1$-many cardinals. 1) Are there cardinals other than $\omega$ with this property? ...
2
votes
1answer
23 views

Clarification of term in graph theory - about star polygon graphs

I was reading about star polygon graphs from the following link: http://mathworld.wolfram.com/StarPolygon.html. As far as I noticed I felt that whenever $d$ is a proper divisor of $n$, then we get ...
3
votes
2answers
87 views

Why is $\cos(x)dx$ a differential form

I am trying to understand the concept of the differential A differential $d$ is a map that sends functions to 1-forms A preliminary example is $$d\sin(x) = \cos(x) dx$$ So the operator $d$ sends a ...
3
votes
1answer
68 views

What does Wolframalpha's definition of “contravariant vector” mean?

http://mathworld.wolfram.com/ContravariantVector.html Wolframalpha offered a one line definition to contravariant vector which is a bit confusing to me Contravariant Vector: The usual type of ...
1
vote
2answers
79 views

What is this categorical notion called?

If we take a category $\mathcal{C}$ of objects with functions as morphisms and restrict the morphisms to injections (monomorphisms?), then this defines a partially ordered set of isomorphism classes. ...
2
votes
3answers
40 views

Terminology for a game in which Black and White have the same “probability” to win

Consider a game between two players, Black and White. The game is sequential and ends after finitely many moves. White moves first. The game ends either in the victory of one of the players or in a ...
0
votes
1answer
127 views

Term for an infinite sequence with both a beginning and an end

How to technically refer to or describe a sequence with both a beginning and an end as well as infinitely many elements between them?       $ a_1 ~,~ a_2 ~,~ a_3 ~,~ \ldots ...
0
votes
2answers
47 views

“Non-trivial element” in factor group terminology

Let $G$ be an abelian group. Let $T$ be the set of elements in $G$ with finite period. ($T$ is called the torsion subgroup of $G$.) Show that $T$ is a normal subgroup in $G$, and show that all ...
2
votes
1answer
51 views

Set of the vertex sets to make connected graph into disjoint sets of vertices?

Suppose a non-directed graph G with vertices V and paths P. What is the name for the vertex sets to make break the graph by removal of some vertices?
2
votes
1answer
37 views

Terminology like “in the direction of $(1, 1, 1)$”

Consider $\text{span}\{(1, 1, 1),~(0, 0, 0)\}$. It's a line through the origin. That much I understand, but why is it "in the direction of $(1, 1, 1)$"? Is it another way of saying $(1, 1, 1)$ lies on ...
2
votes
3answers
103 views

What are these diagrams called? And, what are some good *free* books/notes where I can learn about them?

I ran into the following diagrams while randomly browsing internet I'd like to learn about them.
0
votes
1answer
29 views

If $M$ is a monoid, is there accepted terminology for those elements $x \in M$ satisfying $xM = Mx$?

Suppose $M$ is a monoid and consider an element $x \in M$. Then we call $x$ central iff for all $m \in M$, it holds that $am=ma$. A vast weakening of this condition is to merely require $xM=Mx$. Lets ...
3
votes
1answer
81 views

What does it mean to suppress a number in math?

What does it mean to suppress a number in math? I was doing a math problem and it said to "suppress a term of a sequence." Does this mean to decrease or get rid of the term? Problem: Let ...
5
votes
1answer
95 views

Mathematical meaning of “may not”

Does "may not" mean that never allowed or sometimes not allowed? For example: the sequence may not converge. Does this mean that the sequence never converges or that there is no guarantee that the ...
0
votes
0answers
31 views

Is saying “_The_ invariant subspace” improper?

It's just a question about semantics: does it make sense to refer to the isomorphism between a given vector space and the invariant subspace of a endomorphism or should I say the isomorphism between a ...
2
votes
1answer
52 views

Covariant and Contravariant Functors

In Category Theory, we have covariant and contravariant functors. Mathematically I know the difference between the two - I can picture that. What I would like to know why these concepts are named ...
1
vote
1answer
27 views

Problem 4 from Section E of Chapter 12 of Pinter's Book of Abstract Algebra

The question: Let $f: A\rightarrow B$ be a function, and let $\{ B_i : i \in I\}$ be a partition of $B$. Prove that $\{f^{-1}(B_i):i \in I\}$ is a partition of $A$. My work so far: For any given ...
3
votes
3answers
73 views

Do functions whose domains are infinite sets sequentially or simultaneously map their elements

Here are two equivalent definitions of the axiom of choice Let $x$ be a set. Suppose that if $y,w \in x$, then $y \neq \varnothing$ and $y\cap w = \varnothing$. Then there is a set $z$ such that ...
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votes
3answers
40 views

What is difference between maxima (or minima) and global maxima (or minima)?

I am unable to understand meaning of global maxima (and minima). Are they the same as maxima and minima?
3
votes
1answer
29 views

A Terminology in Group Theory

The term soluble (or solvable) group came from the works of Galois, Abel, Lagrange, relating to solvability of equations by radicals. One may ask then, how the terminology nilpotent group came? The ...